Wow, a lot of good questions I'm not entirely sure I'm totally qualified to answer, but I'll give you my best opinion:
1) He would then be able to upgrade his family's from the poor class to the upper-middle-class". But you didn't. Why?
In my case at least, there were complicated family problems. One of the difficulties with "making it" when everybody you grew up with didn't, is that they all start wanting you to help them. It may not just be money, but often the emotional and psychological problems that having no money brings with it. The short version is, after a few very difficult years I finally realized that what was happening is that they wanted me to live their life and make it work out for them, but I had to live my life and they had to live there's and for a number of years I kept myself (and later my wife) away from my family because of the negative influence they created.
Fortunately, for my parents, over the many years this all happened, they managed to get a bit better at business, eventually sell it and semi-retire. One nice thing about living in a poor area is that you don't need much to retire on!
2) I mean what common prejudices do exist, are the prejudices in favor or against one.
Germans are generally viewed very favorably in the U.S. There's a small fantasy around "German engineering" among most people and the perception that Germans are very intelligent. There's some small lingering feelings about WW2 that's hard to describe, it's not really a bad feeling about Germans, but an arrogant one amongst Americans. However, many Americans have German heritage and are very proud of it. Even if they demonstrate in sometimes silly ways.
As for German schooling and C.S. perception. I think that most Americans honestly don't know how to evaluate it, but assume German C.S. education is as good as American C.S. education (at least among public school education). I don't think any German school in particular is very well known here. Most American will probably believe it's very good since we believe German engineering disciplines in general are very good.
Because of Geography (we really only border two countries, and those are very far away from where most population centers are) and size (Germany is about the same size as New Mexico or Montana), Americans have a very insulated and often ignorant view of the world and foreigners. Sometimes that can be beneficial, sometimes that can be bad for you, but expect that most Americans will know almost nothing about Germany outside of beer, some stereotypes and WW2. If you've never spent much time here, prepare yourself for lots of culture shock. Also, the U.S. is so big that regional areas really do matter, even if everybody looks and talks kind of similar, local attitudes and ideas can be very different.
3) Would you recommend moving to the USA and if so, which state and city should I migrate to?
My wife is an immigrant and I can say that immigrating to the U.S. is not as easy as you might think! Basically you either have to be the immediate family member (child, parent, spouse) of a Citizen or Permanent Resident, or be brought in on an H-1B Visa to do it. Where you end up might have more in relation to those factors than any others.
If you try to come in to do business under a VISA (or the VISA free program we have with Germany) you may be doing something illegal and it can cause all kinds of problems. Being a free-lancer in the U.S. under those conditions can be very legally complicated. http://germany.usembassy.gov/visa/vwp/
If you have a choice, I would avoid Washington D.C. While there's a huge technology industry there, most of the work is for the government and requires citizenship. NYC and the San Francisco area have plentiful jobs, but are very expensive places to live, especially on a starter salary. Secondary cities like Seattle, Boston or Portland might be better as they're looking for people, and the cost of living is much better. I would do lots of job searches and see where there are lots of jobs so you can find an area with a robust job ecosystem.
Be aware, that many states are "at will" hiring states. Meaning they can fire you and you can quit for any reason at all, with no notice. It's not as scary as it sounds in practice, but if that concerns you you might want to research it a bit more.
4) What would I earn there without work experience other than as IT-freelancer? And would that be by other americans as a lot or normal pay?
In theory, even on an H-1B visa, you should earn the same as your peers. But some places will try to take advantage of your situation and underpay you a bit. As to what you salary should be, there's a very helpful website you can use for your research. www.glassdoor.com People anonymously post their job titles, interview experiences and salaries there so you can get an idea what the range should be.
Salary is very nonstandard though, you can find jobs paying as low as $30,000 for entry level and some paying as high as $100,000, depends on location, education, etc. You can live very comfortably in most of the U.S. for $85,000-$100,000, but realistically for a new person in industry you should expect $40,000-$65,000 in most places working as a software developer.
Here is a good chart http://www1.salary.com/Programmer-I-Salary.html
5) I heard that the health system is very expensive over there. Is there a reasonable number of salary that I'd have to earn to not have to worry about that kind of problems?
It is very expensive, especially if you don't have insurance. It's also complicated and confusing. Insurance is starting to be required for everybody and is usually provided by employers for full-time employees. Typically you will pay part of your monthly insurance and the company will pay part of it. For your portion it should run around $100-200/monthly and there's some various out of pocket expenses when you use it. Depending on your insurance, it may not even cover everything and you'll have to pay the difference. Even then, if you have to get a routine operation of some kind (appendix, etc.), it might be cheaper to fly back to Germany and have it done. For small regular doctor things, it's not too bad. Service levels are generally low despite the expense, but the care level is relatively high.
However, it's possible to find the best, most exotic, bleeding edge, medical care, some kind of bizarre new surgery or piece of diagnostic equipment that nobody else in the world has, it'll be available (at a very high price) in the U.S. So if you really need something that severe, and can convince your insurance company to cover it, it might be best to do it here.
One of the problems is that even the doctors can't really tell you how much something will cost. They can try to make it cheaper for you in some ways, but there's a negotiation phase between the insurance company and the medical provider that you don't get to participate in that determines the final bill (and what portion is paid for by insurance).
It's honestly a terrible situation and seems really stupid if you're coming from just about any where in Europe.
Finally) It might be more useful to think of the U.S. as a very tightly integrated EU/Eurozone/Shengen Zone with a more powerful central government and weaker state governments than Europe. It's one country, but the rules and laws are a bit different in every state and each state has it's own central and local governments. So for you, it might be more useful for you to think of each U.S. state as a different country, but they all basically share immigration laws and currency.